Robust biased estimation and its applications in geodetic adjustments

In this paper, a number of robust biased estimators (e.g. ordinary robust ridge estimator, robust principal components estimator, robust combined principal components estimator, robust single-parametric principal components estimator, robust root-root estimator) are established by means of a unified expression of biased estimators and based on the principle of equivalent weight. The most attractive advantage of these new estimators is that they can not only overcome the ill-conditioning of the normal equation but also have the ability to resist outliers. A numerical example is used to illustrate that these new estimators are much better than the least-squares estimator and various biased estimators even when both ill-conditioning and outliers exist. Received: 14 November 1995/Accepted: 11 February 1998     

Determination of post-glacial land uplift from the three precise levellings in Finland

We have calculated vertical velocities and their change in time from three precise levellings in Finland, with central epochs 1902, 1946, and 1986. Models with and without simultaneous determination of heights give the same results for velocities. Evidence for velocity change in time appears at first sight strong but on closer examination turns out to be inconclusive. We offer an alternative explanation in terms of levelling errors and estimate them. A new uplift map closely reproduces main features of earlier maps from partial data, but does not support some details in them. Received: 27 January 1997/ Accepted: 20 April 1998     

Semi-automatic delineation of badlands using contrast in vegetation activity: a case study in the lower Chambal valley,India

Population growth worldwide leads to an increasing pressure on the land. Recent studies reported that many areas covered by badlands are decreasing because parts of badlands are being levelled and converted into arable land. It is important to monitor these changes for environmental planning. This paper proposes a remote-sensing-based detection method which allows mapping of badland dynamics based on seasonal vegetation changes in the lower Chambal valley, India. Supervised classification was applied on three Landsat (Thematic Mapper) images, from 3 different seasons; January (winter), April (summer) and October (post-monsoon). Different band selection methods were applied to get the best classification. Validation was done by ground referencing and a GeoEye-1 satellite image. The image from January performed best with overall accuracy of 87% and 0.69 of kappa. This method opens the possibilities of using semi-automatic classification for the Chambal badlands which is so far mapped with manual interpretations only.     

Separation of global time-variable gravity signals into maximally independent components

The Gravity Recovery and Climate Experiment (GRACE) products provide valuable information about total water storage variations over the whole globe. Since GRACE detects mass variations integrated over vertical columns, it is desirable to separate its total water storage anomalies into their original sources. Among the statistical approaches, the principal component analysis (PCA) method and its extensions have been frequently proposed to decompose the GRACE products into space and time components. However, these methods only search for decorrelated components that on the one hand are not always interpretable and on the other hand often contain a superposition of independent source signals. In contrast, independent component analysis (ICA) represents a technique that separates components based on assumed statistical independence using higher-order statistical information. If one assumes that independent physical processes generate statistically independent signal components added up in the GRACE observations, separating them by ICA is a reliable strategy to identify these processes. In this paper, the performance of the conventional PCA, its rotated extension and ICA are investigated when applied to the GRACE-derived total water storage variations. These analyses have been tested on both a synthetic example and on the real GRACE level-2 monthly solutions derived from GeoForschungsZentrum Potsdam (GFZ RL04) and Bonn University (ITG2010). Within the synthetic example, we can show how imposing statistical independence in the framework of ICA improves the extraction of the ‘original’ signals from a GRACE-type super-position. We are therefore confident that also for the real case the ICA algorithm, without making prior assumptions about the long-term behaviour or on the frequencies contained in the signal, improves over the performance of PCA and its rotated extension in the separation of periodical and long-term components.     

Evaluating the impact of data quantity, distribution and algorithm selection on the accuracy of 3D subsurface models using synthetic grid models of varying complexity

Testing the accuracy of 3D modelling algorithms used for geological applications is extremely difficult as model results cannot be easily validated. This paper presents a new approach to evaluate the effectiveness of common interpolation algorithms used in 3D subsurface modelling, utilizing four synthetic grids to represent subsurface environments of varying geological complexity. The four grids are modelled with Inverse Distance Weighting and Ordinary Kriging, using data extracted from the synthetic grids in different spatial distribution patterns (regular, random, clustered and sparse), and with different numbers of data points (100, 256, 676 and 1,600). Utilizing synthetic grids for this evaluation allows quantitative statistical assessment of the accuracy of both interpolation algorithms in a variety of sampling conditions. Data distribution proved to be an important factor; as in many geological situations, relatively small numbers of randomly distributed data points can generate more accurate 3D models than larger amounts of clustered data. This study provides insight for optimizing the quantity and distribution of data required to accurately and cost-effectively interpolate subsurface units of varying complexity.     

Negotiating on location, timing, duration, and participant in agent-mediated joint activity-travel scheduling

Agent-based simulation has become an important modeling approach in activity-travel analysis. Social activities account for a large amount of travel and have an important effect on activity-travel scheduling. Participants in joint activities usually have various options regarding location, participants, and timing and take different approaches to make their decisions. In this context, joint activity participation requires negotiation among agents involved, so that conflicts among the agents can be addressed. Existing mechanisms do not fully provide a solution when utility functions of agents are nonlinear and non-monotonic. Considering activity-travel scheduling in time and space as an application, we propose a novel negotiation approach, which takes into account these properties, such as continuous and discrete issues, and nonlinear and non-monotonic utility functions, by defining a concession strategy and a search mechanism. The results of experiments show that agents having these properties can negotiate efficiently. Furthermore, the negotiation procedure affects individuals’ choices of location, timing, duration, and participants.